The hydrodynamic stability of ionization-shock fronts - Linear theory

Abstract

The hydrodynamic stability of an ionization-shock front is investigated in the case where all regions are taken as isothermal and self-gravity is neglected. The evolving, unperturbed state is described by a similarity solution. A technique is developed which reduces the stability problem from a system of partial differential equations and associated boundary conditions to a coupled set of ordinary differential equations with time-dependent coefficients. This approach is shown to be valid as long as the perturbation wavelength is much greater than the thickness of the ionization-shock front. Perturbations are considered to arise from density inhomogeneities in the ambient medium. Numerical results along with an approximate analytic solution are given and show a new instability whereby all wavelengths greater than several recombination lengths grow without bound in an oscillatory manner. However, the wavelength with the fastest growth rate increases as the system evolves. A short discussion on the physical mechanism involved and several observational aspects, including a comparison with the morphology of the California nebula, is presented. The results suggest that this instability can produce irregular structures similar to the bright rims and elephant trunks seen in many diffuse nebulae.